A proposed solar panel installation for the roof of a house has the following sp

Question

A proposed solar panel installation for the roof of a house has the following specifications

Number of panels: 12
Maximum output power: 190 W / panel
Average output (over the year) 120 W / panel
Average hours of generation: 7hr / day
Efficiency of inverter: 0.95 (outputs power for house or for sale)
Cost of the installation: $6000
Price of electricity (to buy): $0.22 /kWh (purchased from the electricity company)
Price of electricity (sold): $0.44 / kWh (sold to the electricity company)

i) On average how many kWh of usuable energy (out of the inverter) is expected from the installation in 1 Year?

ii) Assume all the energy generated by the solar installation was consumed by the household, instead of buying electricity from the electricity company. How long will it take for the owner to break even on this investment? (Assume the owner pays cash for the installation and ignore inflation)

iii) Assume that 80% the energy generated by the solar installation was sold to the electricity company during the day, the other 20% being consumed by the household. How long will it take for the owner to break even on this investment (Assume owner pays cash for the installation and ignore inflation)

iv) If the owner was to install batteries to store the 80% excess energy generated during the day, so it could be used at night when the household consumes most of its energy. Even if the batteries had an efficiency of 10.0, explain why this would not be cost effective interms of the cost per kWh

Explanation / Answer

(i) total average power generated over the year by the inverter = 12*120*7*365*0.95*0.001 = 3495.24 kWh (ii) cash saver per year = 0.22*3495.24 = $768.9528 time to break even = (6000/768.9528) = 7.801 years (iii) cash saved per year = 3495.24[(0.22*0.2)+(0.44*0.8)] = $1384.11504 time to break even = (6000/1384.11504) = 4.335 years (iv) this will not be cost effective in terms of cost as efficiency of batteries is very low. even if he saves 80% of excess energy ( which is 2796.192 kWh ) in batteries he will only be able to use 10% (which is 279.6192 kWh). when he installs batteries he saves only the cost of 20% of power generated and the cost for 279.6192 kWh which is $215.31 If he doesn't install batteries he can save $1384.12. clearly installing batteries is not cost-effective

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